D₃×C₃⋊#1084 #14518780

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₃²

Aliases

direct product	D₃×C₃⋊#1084
unambiguous semidirect product	(C₃×D₃)⋊#1084

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₃×C₃⋊(C₃⋊D₃)
commutator, hypocenter	C₃²×H(3,𝔽₃)	C₂×C₄
Fitting, cosocle	C₂×C₃²×H(3,𝔽₃)	C₂²
socle	C₂×C₃³	C₂×C₃⋊D₃
prime radical	C₂×C₃×D₃×H(3,𝔽₃)	C₂
LCS	G ▷ C₃²×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

1205 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

normal subgroups only

This group has 1205 conjugacy classes of subgroups — too many to draw. Only its 214 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3174);